# PCM : Picard Consistency Model for Fast Parallel Sampling of Diffusion Models

arXiv: https://arxiv.org/abs/2503.19731 · HTML: https://mlsanity.com/paper/2503.19731/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 38 of its 47 references that are in the map.
- First posted on arXiv 25 Mar 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 38)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [Make-An-Audio: Text-To-Audio Generation with Prompt-Enhanced Diffusion Models](https://mlsanity.com/paper/2301.12661/) (2023)
- [Break the Sequential Dependency of LLM Inference Using Lookahead Decoding](https://mlsanity.com/paper/2402.02057/) (2024)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [Speculative Decoding with Big Little Decoder](https://mlsanity.com/paper/2302.07863/) (2023)
- [SpecTr: Fast Speculative Decoding via Optimal Transport](https://mlsanity.com/paper/2310.15141/) (2023)
- [Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2305.16317/) (2023)
- [DALL-E-Bot: Introducing Web-Scale Diffusion Models to Robotics](https://mlsanity.com/paper/2210.02438/) (2022)

## Built on by (most cited first, 2 of 2)

- [Just-in-Time: Training-Free Spatial Acceleration for Diffusion Transformers](https://mlsanity.com/paper/2603.10744/) (2026)
- [Accelerating Discrete Diffusion Models with Parallel-In-Time Sampling](https://mlsanity.com/paper/2607.00773/) (2026)

## Abstract (arXiv)

Recently, diffusion models have achieved significant advances in vision, text, and robotics. However, they still face slow generation speeds due to sequential denoising processes. To address this, a parallel sampling method based on Picard iteration was introduced, effectively reducing sequential steps while ensuring exact convergence to the original output. Nonetheless, Picard iteration does not guarantee faster convergence, which can still result in slow generation in practice. In this work, we propose a new parallelization scheme, the Picard Consistency Model (PCM), which significantly reduces the number of generation steps in Picard iteration. Inspired by the consistency model, PCM is directly trained to predict the fixed-point solution, or the final output, at any stage of the convergence trajectory. Additionally, we introduce a new concept called model switching, which addresses PCM's limitations and ensures exact convergence. Extensive experiments demonstrate that PCM achieves up to a 2.71x speedup over sequential sampling and a 1.77x speedup over Picard iteration across various tasks, including image generation and robotic control.